Category Archives: History of science

I expected better of Tim Radford

Tim Radford is a science writer who works for The Guardian newspaper. In fact many people consider him the best British science writer of the current crop, not without a certain amount of justification. Because of this I was, as a historian of science, more than disappointed by the opening paragraph of his latest post on the science section of the Guardian’s website, a book review: “The Copernicus Complex by Caleb Scharf review – a cosmic quest”. Radford opens his review with three sentences of which the third caused me to groan inwardly and bang my head in resignation on my computer keyboard.

The Copernican principle changed everything. It was not formulated by Copernicus, who in 1543 proposed only that the Earth was not the centre of the universe, and that the motion of the Earth around the sun could explain the irregularities in the heavens. At the time, ideas like that could get people condemned to the stake. [my emphasis]

I ask myself how much longer historians of science are going to have to keep repeating that this statement is complete and utter rubbish before science writers like Tim Radford finally take their hands off their ears and the blinkers from their eyes and actually accept that it is wrong. No Mr Radford, an astronomer or cosmologist in the sixteenth-century suggesting that we live in a heliocentric cosmos rather than a geocentric one was not in danger of being condemned to the stake and yes there is solid historical evidence, which apparently you choose to ignore in favour of your fantasies, to prove this. Let us briefly review that evidence for those, like Tim Radford, who have obviously not been paying attention.

Already in the fifteenth- century Nicholas Cusanus openly discussed various aspects of the heliocentric hypothesis in his works, presenting them in a favourable light. Was he condemned to the stake for his audacity? No he was treated as an honoured Church scholar and appointed cardinal.

Let us move on to the subject of Radford’s highly inaccurate statement, Copernicus, like Cusanus a cleric and a member of the Church establishment, how did the Church react to his provocative heliocentric claims? In 1533 the papal secretary, Johann Albrecht Widmannstetter held a lecture on Copernicus’ theories to Pope Clemens VII and assembled company in the papal gardens. We assume this was based on Copernicus’ Commentariolus, the manuscript pamphlet of his ideas written around 1510, as De revolutionibus wasn’t published until 1543. Was he condemned to the stake for his rashness? No, Clemens found much favour in his lecture and awarded him a valuable present for his troubles. Two years later Widmannstetter became secretary to Cardinal Nikolaus von Schönberg, an archbishop and papal legate, who had been present at that lecture. In 1536 Schönberg wrote a letter to Copernicus urging him to make his theories public and even offering to pay the costs of having his manuscript copied. Not a lot of condemning to the stake going on there. Copernicus had Schönberg’s letter printed in the front of De revolutionibus.

Dear Tim Radford I am sure that as a topflight science writer you check the scientific facts in the articles that you write very carefully to ensure that you are not misleading your many readers. May I humbly request that in future you pay the same attention to the historical facts that you publish so as not to serve up your readers with pure unadulterated historical hogwash?

P.S. If anybody mentions either Giordano Bruno or Galileo Galilei in the comments I will personally hunt them down and beat them to death with a rolled up copy of The Guardian.




Filed under History of Astronomy, History of science, Myths of Science, Renaissance Science

Galileo, Foscarini, The Catholic Church, and heliocentricity in 1615 Part 2 –the consequences: A Rough Guide.

In part one I outlined the clash, which took place between Galileo and Foscarini on the one side and the Catholic Church on the other in the second decade of the seventeenth-century. I ended by saying that this initial confrontation had very few consequences for Galileo at the time, who continued to be the highly feted darling of the North Italian in-crowd, including the higher echelons of the Catholic Church. Of course the events of 1615/16 would come back to haunt Galileo when he was tried for writing and publishing his Dialogo in the 1630s but that is a very complex topic that require a post of its own sometime in the future. I also wrote that the books of Foscarini and of the Protestant Copernicans, Michael Maestlin and Johannes Kepler were placed on the Index of Forbidden Books. Interestingly De revolutionibus was only placed on the Index until corrected. It is here that we will pick up the thread and examine the consequences of the Church’s actions on the development of astronomy in the seventeenth-century.

What did it mean when I say that De revolutionibus was only placed on the Index until corrected? This means that De revolutionibus was not forbidden but that only those statements within the book, which claimed that heliocentricity was a proven fact, were to be removed. This mild censorship, only a handful of passages in the whole book were affected, was carried out comparatively quickly and the thus censored version was given free to be used by astronomers already in 1621. The whole of this episode demonstrates that the powers that be within the Church were well aware that De revolutionibus was an important astronomical text and should, despite the judgement of the eleven members of the commission set up to adjudicate on the affair that the idea that the Sun is stationary is “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture…”; while the Earth’s movement “receives the same judgement in philosophy and … in regard to theological truth it is at least erroneous in faith”, remain available to Catholic astronomers for their studies.

There is a widespread popular perception that the Church’s theological rejection of the theory of heliocentricity led to a breakdown of astronomical research in Catholic countries in the seventeenth-century. Nothing could be further from the truth. As mentioned in the first part of this post, some historians think that Cardinal Bellarmino’s admission in his letter to Foscarini that … if there were a real proof that the Sun is in the centre of the universe, that the Earth is in the third sphere, and that the Sun does not go round the Earth but the Earth round the Sun, then we should have to proceed with great circumspection in explaining passages of Scripture which appear to teach the contrary …, was interpreted by many Jesuit and Jesuit educated astronomers as a challenge to find an empirical proof for heliocentricity. As we shall see there is quite a lot of circumstantial evidence to support this claim.

An important historical fact to be born in mind when considering the development of astronomy in the seventeenth-century was that there existed no empirical proof for the heliocentric hypothesis, whether it be in the original form proposed by Copernicus or the much more sophisticated form developed by Kepler. The astronomers would have to wait until 1725 before James Bradley delivered the first proof of the earth’s annual orbit around the sun with his discovery of stellar aberration and slightly longer before the geodesists demonstrated that the earth is an oblate spheroid thus confirming a prediction made by both Newton and Huygens that diurnal rotation would result in the earth having this form thus proving indirectly the existence of diurnal rotation. This tends to be forgotten or simply ignored by those claiming that the Church should have accepted heliocentricity as a fact in 1615. In reality the heliocentricity became accepted by almost all astronomers whether Catholic or non-Catholic by around 1660, long before any empirical proof existed, on the basis of accumulated circumstantial evidence and the lack of a convincing alternative. A lot of that circumstantial evidence was delivered by Catholic astronomers, who despites the Catholic theological position, continued to work avidly on the development of the modern astronomy.

It is also important to realise that although the Church banned claiming that heliocentricity was a fact, the heliocentric theory, it was still perfectly possible to speculate about heliocentricity, the heliocentric hypothesis. Throughout the seventeenth-century Catholic astronomers in Italy adopted an interesting strategy to deal with the Church’s ban of the heliocentric theory. They would preface their works with a statement of the fact that in its wisdom the Church had shown the heliocentric theory to be contrary to Holy Scripture and thus factually false and then proceed to discuss this interesting mathematical hypothesis without claiming it to be true. This strategy sufficed for the Inquisition’s guardians of the truth and thus the astronomers continued to discuss and disseminate heliocentricity with impunity.

Scientific theories are not only disseminated by their supporters but often also by their opponents. Long before Galileo muddy the waters with his heated challenge to the Church’s exclusive right to interpret the Bible it is certain that more people learnt of the existence of the heliocentric hypothesis and its basic details from the works of Christoph Clavius, a convinced defender of geocentricity, than from De revolutionibus. In his commentary on the Sphere of Sacrobosco, an introductory astronomy textbook, Clavius discussed Copernicus’ heliocentric hypothesis sympathetically, respecting its mathematical sophistication, whilst firmly rejecting it. This book went through numerous editions and was the most widely disseminated and read, by both Catholic and Protestant students, astronomy textbook throughout most of the seventeenth-century and was for many their first introduction to the ideas of Copernicus. It was also Clavius’ postgraduate students, in his institute for mathematical research at the Collegio Romano, who provided the very necessary empirical confirmation of Galileo’s telescopic discoveries in 1611, shortly before Clavius’ death. This activity by Jesuit astronomers pushing the boundaries of astronomical knowledge did not cease following the decisions of 1616.

There was a slowdown in the development of modern astronomy in the second and third decades of the seventeenth-century that has nothing to do with the Church’s ban but was the result of a lack of technological advance. In the four years between 1609 and 1613 European astronomers had discovered everything that it was possible to discover using a Dutch or Galilean telescope with a convex objective and a concave eyepiece. The only new discoveries were the observations of a transit of Mercury by Gassendi in 1631 and a transit of Venus by Horrocks in 1639 neither of which had an immediate impact because they didn’t become widely known until much later. For various reasons, not least Galileo’s very public rejection of it as inferior, the superior Keplerian or astronomical telescope, with two convex lenses, didn’t start to become established until the 1640s. However once established the new discoveries began to flow again: the moons of Saturn, the rings of Saturn, diurnal rotation of the planets. Many of these new discoveries, which added new circumstantial evidence for heliocentricity, were made by Giovanni Domenico (Jean-Dominique) Cassini (1625–1712) a Jesuit educated Catholic astronomer. It was also Cassini, with the support of his teachers the Jesuits Giovanni Battista Riccioli and Francesco Maria Grimaldi, who proved, using the heliometer constructed for this purpose in the San Petronio church in Bologna, that either the sun’s orbit around the earth or the earth’s orbit around the sun must be an ellipse, as required by Kepler. Although this proved that the orbit is an ellipse it didn’t show which system was correct.

Cassini, who would go on to become the leading observational astronomer in Europe, always avoided committing himself to any systems simply delivering empirical results and leaving the cosmological interpretation to others. Although confirming Cassini’s heliometer results Riccioli stayed committed to semi-Tychonic system, in which the inner planets orbited the Sun, which in turn together with Saturn and Jupiter orbited the Earth. Riccioli presented this rather bizarre mongrel in his Almagestum Novum published in 1651. Riccioli’s Almagestum contained descriptions of all the various possible systems, including the Copernican, and became a very widely disseminated and read technical textbook for astronomers, both Catholic and Protestant. Like Clavius before him, Riccioli introduced many to heliocentricity for the first time. The Almagestum contained 126 arguments concerning the Earth’s motion 49 pro and 77 contra the most extensive discussion of the problem ever. You can read Chris Graney’s English translation of the arguments here. Although Riccioli came out against heliocentricity his analysis was sympathetic enough to the concept that he was actually investigated by the Inquisition.

Having been made available by the Index copies of De revolutionibus appear only to have been actually censored within Italy nearly all the surviving censored copies, including Galileo’s, coming from there. Outside of Italy, with the notable exception of Descartes, nobody seems to have taken very much notice of the Inquisition’s ban. Descartes appears to have withheld publication of his The World, in the 1630s, containing his defence of heliocentricity, out of respect for his Jesuit teachers. Publishing his views, in modified form, first in his Principles of Philosophy in 1644.

Another Frenchman, Pierre Gassendi like Descartes educated by the Jesuits, who became professor of mathematics at the Collège Royal in Paris in 1645 published his views on astronomy in his Institutio astronomica, although formally a supporter of the Tychonic system, Gassendi’s presentation of the Copernican system is so sympathetic that many historians have interpreted him as a secret supporter of heliocentricity. Gassendi also published biographies of Tycho, Peuerbach, Regiomontanus and Copernicus. Like Riccioli, Gassendi’s astronomical writings were very popular and very widely read, again leading to a widespread dissemination of the principles of heliocentricity.

Another leading French Catholic astronomer, Ismael Boulliau was an open and avid supporter of the Keplerian elliptical astronomy and was indeed the first to hypothesise that gravity ought to be an inverse quadrate force, a significant step in the road to acceptance of heliocentricity. It was Boulliau’s dispute with the English astronomer Seth Ward about Kepler’s second law, which nobody liked, both parties offering alternatives, that first made Newton aware of Kepler’s system.

By about 1660 enough circumstantial evidence had been accumulated that most astronomers in Europe both Catholic and Protestant, with the necessary education to do so, had accepted heliocentricity as a fact with a small minority still holding out for a Tychonic system. In the end the Tychonic system had fallen victim of Ockham’s razor being viewed as overly complex in comparison with the Keplerian elliptical system for which more and more evidence had accumulated throughout the preceding fifty years. A significant advance in the development of modern physics in which Galileo’s Discorsi had played an important role also contributed crucially to this acceptance, dealing as it did with the physical problems of terrestrial motion. A detailed analysis of these developments would make this already over long post even longer and must be dealt with separately.

Although by no means an exhaustive presentation of the development of astronomy in the seventeenth-century, I think the above contains enough to demonstrate that the Church’s ban of the heliocentric theory had very little negative influence on that development and that Catholic astronomers played a leading role within it. Returning to my earlier speculation, I feel justified in saying that had Galileo and Foscarini not forced the Church’s theologians into a corner in 1615, then the Catholic astronomers, and in particular the Jesuits and their pupils, would have led the Church to an acceptance of heliocentricity within the seventeenth-century.




Filed under History of Astronomy, History of science, Myths of Science

“…realigning the heavens with a single stroke of the brush.“ – Really?

Recently on twitter I stumbled across a problematic discussion, as to which single image had most changed the course of science. Although the various participants made stimulating and interesting suggestions, Darwin’s tree diagram, Franklin’s photo of DNA etc. I found this discussion problematic because it suffers from the same difficulties as discussion in the history of science as “the first”, “the greatest”, “the father of” and all similar hyperbolic claims, just how do you measure and compare the numerous candidates that spring to mind?

This discussion didn’t just appear out of cyberspace on somebody’s whim but was provoked by Joe Hanson at It’s OK to be Smart and his post Message from the Moon, which in turn was provoked by the set of washes of the moon by Galileo that had been circulating on Twitter a couple of days before.

Galileo's washes of the moon.

The watercolour sketches that Galileo made of his initial telescopic observations of the moon in 1609/10 are iconic images in the history of science that did have a major impact on the way humanity viewed the cosmos but there are an awful lot of inaccuracies in Hanson’s description of that impact that I am going to analyse here.

Hanson’s first minor error is to claim that the images he has posted on his blog are included in the Sidereus Nuncius. Galileo’s legendary publication does indeed included woodcuts of five of his lunar watercolours but the sheet displayed by Hanson, and here above, was not included, a trivial but important point.

Hanson informs us:

But hiding in their shadows lies a greater significance. The squiggled edges of that bleeding ink bear an observation that altered the heavens themselves. Or at the very least, our view of them.

And then goes on to explain why:

In 1610, cosmology, not that it had much to show for itself as a science, was still based on the ideas of Aristotle, who by this time had been dead for 18 centuries. So current! Copernicus’ observation that the Earth orbited the sun, first published in 1543, had begun to challenge Aristotelian supremacy, it wasn’t exactly a popular idea. 

Aristotle’s cosmological beliefs were based on the idea that the heavens were made of a perfect substance called “aether”, and therefore the circular motions and spherical shapes of heavenly bodies were also perfect. Earth, he claimed, was inherently imperfect, as were all the things that existed upon it. Everything in the heavens was awesome, and Earthly matter was inherently “just okay”, even if its name was Aristotle. This was one of the reasons people found Copernicus’ claims so hard to swallow. The imperfect Earth among the perfect heavens? Heresy! [emphasis in original]

Somewhat sloppily expressed but so far so good, although placing the earth in the heavens didn’t really play that much of a role in the initial rejection of Copernican cosmology being insignificant in comparison to the physical problems engendered by a moving earth. Hanson’s argument is that because Galileo’s interpretations of what he saw through his telescope, and don’t forget that they are interpretations, clearly suggested that the moon was not smooth and perfect but had a landscape like the earth he had realigned “the heavens with a single stroke of the brush”; a nice literary figure of speech but unfortunately one that doesn’t fit the historical facts.

Already in antiquity people, had speculated that the differing shades of the moons surface were the result of a mountainous landscape. This viewpoint was expressed most notably by Plutarch in his On The Face Which Appears in the Orb of the Moon, one of his collection of essays, the Moralia. This was well known and widely read in the sixteenth-century and was even used by Kepler as a springboard for his own “lunar geography”, the Somnium, written but not published before Galileo made his telescopic discoveries. This widespread alternative concept of the lunar surface made it much easier to accept Galileo’s discovery and considerably weakened any impact that it might have had on Aristotelian cosmology. However this was not the only factor that gives the lie to Hanson’s “single stroke of the brush” postulate. Aristotle’s division of the cosmos into two spheres one superlunar, which was perfect, unchanging and eternal, everything below, and the other sublunar, which was imperfect, constantly changing and subject to decay had been under attack for most of the century preceding Galileo’s discoveries, as I have already outlined in my post on Comets and Heliocentricity.

In the 1530s observations of several comets had led many leading European astronomers to the conclusion that comets were superlunar phenomena and not sublunar ones as Aristotle’s cosmology required. Comets are of course anything but perfect, unchanging and eternal. In the 1570s another generation of European astronomers, Tycho Brahe and Michael Maestlin to the fore, confirmed this conclusion making life more than somewhat difficult for any cosmologist who wished to maintain a strict Aristotelian party line. To make matters worse the stellar novae of 1572 and 1604 observed once again by Europe’s finest watchers of the heavens and determined by them to be unquestionably superlunar really put the kibosh on Aristotle’s wonderful division of the cosmos. All in all by 1610 Aristotle’s cosmology was already looking distinctly unhealthy and Galileo’s discovery of the lunar landscape far from being an unexpected deadly bolt out of the blue was just another blow helping it on its way to its grave.

Hanson might be forgiven for his over emphasis of the impact of Galileo’s lunar watercolours based obviously on his ignorance of Renaissance astronomical and cosmological history but the content of his closing paragraph displays an ignorance that I, for one, find hard to forgive. Our intrepid non-historian writes:

Galileo’s Sidereus Nuncius [emphasis in original] also included newly detailed maps of the constellations and the mention of four moons of Jupiter (although detailed observations of those were still centuries away), [my emphasis] but it was his drawings of our moon that bore the most impact on future astronomical science, realigning the heavens with a single stroke of the brush.

Having over emphasised the significance of the impact of Galileo’s lunar watercolours Hanson dismisses his discovery of the moons of Jupiter in a throwaway comment. He couldn’t demonstrate his ignorance of the material more spectacularly.

It was of course Galileo’s discovery of the four largest moons of Jupiter that caused the sensation and also did the most damage to Aristotelian cosmology, when he published the Sidereus Nuncius in 1610. Central to Aristotelian cosmology was the principle of homo-centricity, i.e. the concept that all celestial bodies, the sphere of the fixed stars and the seven planets, revolve around a common centre, the earth. The discovery of the Galilean moons, as they came to be known, was a direct empirical proof that the principle of homo-centricity was wrong. It lent indirect support to heliocentricity, which required two centres of revolution the sun for the fixed stars and the six planets and the earth for the moon. It was Galileo’s discovery of the Medician Stars, as he called them, which led to his much desired appointment as court philosophicus and mathematicus in Florence and professor of mathematics at the University of Pisa without teaching duties. Catapulting him almost overnight from being an obscure, ageing professor of mathematics to being Europe’s most notorious astronomer. The four moons of Jupiter are not “mentioned” in Sidereus Nuncius they are the reason for its hurried and secretive, to prevent anybody else beating him to the punch, composition and publication.

The illustrations of the moon in the Sidereus Nuncius are the eye candy, which the reader can admire but the far less visually spectacular diagrams of the positions of the four moons relative to Jupiter are the explosive content that make this slim pamphlet one of the most important scientific publications of all time and elevated Galileo into the pantheon of scientific heroes.

Page from Galileo's observation log displaying position of the moons relative to Jupiter

Page from Galileo’s observation log displaying position of the moons relative to Jupiter


Filed under History of Astronomy, History of science, Renaissance Science

How much can you get wrong in an eight hundred word biographical sketch of a very famous sixteenth and seventeenth-century mathematicus and philosophicus? – One helluva lot it seems?

If someone is doing the Internet equivalent of being a big-mouthed braggart and posting an article with the screaming title, “10 Absurdly Famous People You Probably Don’t Know Enough About” you would expect them to at least get their historical facts right, wouldn’t you? Well you would be wrong at least as far as “absurdly famous” person number seven is concerned, Galileo Galilei. Tim Urban the author of this provocative article on the ‘Wait But Why’ blog appears to think that history of science is something that you make up as you go along based on personal prejudice mixed up with some myths you picked up some night whilst drunk in a bar. Having not had a real go at somebody else’s terrible history of science for sometime now and not having deflated my favourite punching bag, Galileo or rather the hagiographic imbeciles who write about him, for even longer I thought I would kill two birds with one stone and correct Mr Urban’s little piece as it were a high school term paper. The blue text is original Urban the black comments are mine.


Lived: 1564 – 1642

He makes a promising start in that he at least got the years of birth and death right, although with the same amount of effort he could have given us the exact dates – 15 February 1564 – 8 January 1642

In 11 words: Rare giant of scientific advancement fighting against hopelessly-backward Catholic Church

After that reasonably good beginning we go rapidly down hill. As I have commented on a number of occasions Galileo was by no means as rare or as gigantic as he is usually painted. He also spent most of his life getting along very happily with the Catholic Church with whom he was on good terms and which was in a lot of things, including scientific one, anything but hopelessly-backward. Just to quote one example about which I’ve blogged in the past, it was the Jesuit astronomers at the Collegio Romano who delivered the very necessary scientific confirmations of Galileo’s telescopic astronomical discoveries and then invited Galileo to Rome to celebrate them.

His main thing: Einstein called Galileo “the father of modern science,” which sums things up pretty nicely.

Einstein, as a leading historian of Renaissance science is of course highly qualified to make such a judgement. Regular readers of this blog should by now know my opinion of such expressions as “the father of” and in particular their use to describe Galileo. For those that don’t I recommend my post, “Extracting the stopper”, as a good starting-point.

Galileo made major discoveries about the motion of planets and stars, the motion of uniformly accelerated objects (i.e. that two objects would fall at the same rate regardless of their masses), sound frequency, and the basic principle of relativity, among other things

I must admit to being somewhat perplexed by the claim that Galileo made “major discoveries about the motion of planets and stars”; I’m not aware of any achievements by the good man in this direction, perhaps somebody could enlighten me?

—and major advancements in technology, including inventing or improving upon the telescope, microscope, thermometer, pendulum, and the compass.

Galileo made an improved telescope and might have been one inventor of the microscope, although this is clouded in uncertainty. He experimented with a thermoscope, not a thermometer, but probably did not invent it. He neither invented nor improved the pendulum and I don’t think he or anybody else ever claimed that he did so. He did however investigate the properties of the pendulum, although the law he set out for the pendulum is actually wrong.

The last claim is quite funny and turns up time and time again quoted by people who literally don’t know what they are talking about. Galileo had nothing to do with the (magnetic) compass but manufactured and marketed an improved version of the sector, or proportional or military compass. This is a hinged ruler with numerous scales used for making mathematical calculations particularly by artillery officers. This instrument has several independent inventors; the one improved by Galileo was invented by his mentor, Guidobaldo del Monte.

Galileo's military compass

Galileo’s military compass

His work was central to most future developments in science, including those of Newton and Einstein, and most of what he discovered was in contradiction with conventional wisdom—his work was as shocking and revolutionary in the 1600s as Einstein proclaiming that “time is relative” was in the 1900s.

This is typical of the hagiographical hogwash dished up by people writing about Galileo. The only part of Galileo’s work ‘central’ to Newton was the parabolic flight path of projectiles, which was discovered independently by other including Thomas Harriot. His only connection to Einstein is the rejection of Galilean relativity in the theory of the latter. Very little of Galileo’s own work was shocking and the only parts that were in anyway revolutionary were the laws of fall, discovered independently and earlier by Benedetti, and heliocentricity, a field in which Galileo was not the discoverer or inventor but merely the polemicist, who probably did more damage than good through his advocacy.

But the most impressive part about Galileo, other than his ability to make such a cranky facial expression in the above painting, is that he did everything he did in the face of threats and repression by the Catholic Church and their inane loathing of ground breaking scientific advancements.

I begin to get the impression that our author has a personal problem with the Catholic Church, which did not have an “inane loathing of ground breaking scientific advancements”, and except in the one case Galileo did nothing in “the face of threats and repression by the Catholic Church” but actually received much support and encouragement from many leading figure in the Church hierarchy for the vast majority of his life and work.

The main thing the Church kept yelling at Galileo for was his backing and advancement of Copernicus’s heliocentric model of the universe, which puts the sun, instead of the Earth, in the center of the solar system and suggests that the Earth’s spinning is why the sun appears to revolve around the Earth. The Church declared heliocentrism to be “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture”—in particular, the parts of scripture that said things like, “the world is firmly established, it cannot be moved” and “the Lord set the earth on its foundations; it can never be moved”—and ordered Galileo “to abstain completely from teaching or defending this doctrine and opinion or from discussing it… to abandon completely… the opinion that the sun stands still at the center of the world and the earth moves, and henceforth not to hold, teach, or defend it in any way whatever, either orally or in writing. “That would be like modern-day governments imprisoning geologists who studied ancient rocks because their findings conflicted with the Bible’s accounts of the Great Flood. Or like preventing gay people from getting married because of passages in the Bible about sexual orientation. Thankfully, those times are over.

The above paragraph contains the real reason that Mr Urban is frothing at the mouth about the Catholic Church, Galileo’s clash with the Church on heliocentricity. Once again I’m not going to go into great detail about the whole sad sorry affair but will for the umpteenth time repeat that the central problem had very little to do with science, astronomy, cosmology or whatever but with the fact that in 1615 Galileo tried to tell the Church how to interpret the Bible. If he had not done this and instead bided his time patiently, as suggested by his friends, including Cardinal Maffeo Barberini the later Pope Urban VIII, the Church would in its own time almost certainly have adopted heliocentricity. Instead of which through Galileo’s pig-headedness the acceptance of heliocentricity by the Catholic Church was delayed by about one hundred and fifty years.

So the Church repressed the greatest genius of the century,

There’s no such thing as the greatest!

… finding him “vehemently suspect of heresy,” and placed him under house arrest for the rest of his life. Luckily, Galileo just hung out on his couch and kept doing his thing, publishing some of his most important works while under house arrest.

I know Galileo fans and militant atheists don’t like to hear this but, for the ‘crime’ of which he was found guilty, Galileo was treated very, very gently and his sentence was very mild.

Other things:

  • Galileo never married, having all three of his children out of wedlock with the same woman.
  • We got something right!
  • One of the reasons Galileo started inventing things (like the telescope) in the first place was that he badly needed money to deal with all the money his starving artist little brother kept “borrowing” from him.
  • Like many Renaissance mathematicians Galileo supplemented his income by designing, manufacturing and selling scientific instruments. He didn’t invent the telescope! Galileo was notoriously always short of money not because he supported his little brother financially, which he did, but because he enjoyed the good life and tended to live beyond his means.
  • He was briefly a professor at the University of Pisa, but he was inappropriate with his students and the university didn’t renew his contract.
  • The second part of the above sentence is a pure fabrication. Galileo was professor of mathematics in Pisa from 1589 till 1592 when he applied for and received the more prestigious and better-paid professorship for mathematics in Padua where he remained until 1610.
  • Despite his conflicts with the Church, Galileo was a devout Catholic. He briefly became a priest before his father convinced him to go into medicine, and his two daughters were nuns. But he was critical of the Church’s repression of science, stating, “Holy Writ was intended to teach men how to go to Heaven, not how the heavens go.”
  • That Galileo was a devout Catholic is a standard claim in the history of science repeated, I think, to make the Church look worse for their persecution of the man. This claim has been strongly challenged by Renaissance historian; David Wootton in his biography “Galileo: Watcher of the Skies” (Yale University Press, 2010), which paints Galileo convincingly as a very lax Catholic and possibly an unbeliever. Galileo was never a priest but did spend a few months in a monastery as a teenage novice, although he never took holy orders. Galileo’s two daughters were placed in a monastery because, being illegitimate, he considered them unmarriageable and also to spare him the cost of their dowries, a standard procedure in that period.
  • One of Galileo’s worst offenses against the Church was creating a character called Simplico in his famous book Dialogue Concerning the Two Chief World Systems, who always presented the old, incorrect, geocentric view. Simplico suggests “simpleton” in Italian just like it does in English, and in the book, Simplico does not come off very well. The issue is that a lot of what Simplico says in the book were well known to be the direct views of the Pope (Urban VIII), indirectly insulting the Pope and hastening Galileo’s path toward house arrest.
  • The character in the Dialogo who presents the case for geocentricity is called Simplicio not Simplico. The insult of the Pope was much more direct than suggested here. When Urban VIII granted Galileo permission to write a book explaining both geocentricity and heliocentricity, in order to prove that Catholics were not ignorant of the latter theory, he specifically instructed Galileo to include his own theological argument against deciding for one system over the other because this would “limit and restrict the Devine power and wisdom to some particular fancy of my own”. A not unreasonable viewpoint given that there were no proofs for the heliocentric system at that time. Galileo did as instructed including exactly those words in the final speech of Simplicio, the simpleton, on the last page of the book, who had had seven kinds of intellectual shit kicked out of him in the preceding four hundred pages (in the edition I own) by the other two characters. This really reduced Urban’s argument to a joke! Not a smart move, Signore Galilei.
  • It wasn’t until 200 years later in 1835 that the Church finally stopped its prohibition of books advocating heliocentrism and not until 1992 that the Vatican officially cleared Galileo’s name of any wrongdoing.
  • The church allowed the publication of an edition of Galileo’s works, excluding the Dialogo, in 1718 just 76 years after his death. In 1741 a complete edition of his works was authorised by Pope Benedict XIV. The general ban on works advocating heliocentricity was lifted in 1758.
  • It should be noted that Galileo’s church difficulties occurred in the heart of the Renaissance. You can only imagine what it was like to be a scientist in the far more repressive Middle Ages (and how much potential scientific advancement was stifled).
  • We’re back in anti-Church bullshit city! Within the history of science Galileo’s difficulties with the Church, which he largely brought down on his own head, remain a largely isolated incident. The Middle Ages were by no means more repressive than the Renaissance and in fact much scientific progress was made during the Middle Ages, following the re-establishment of an urban culture around 1000 CE. Also it should be noted that the majority of that progress was made by members of the Catholic Church. Galileo was very much aware of the work of his medieval predecessors and built his own work on the foundations that they had constructed.
  • Some weirdo cut the middle finger off of Galileo’s corpse a century after his death, and it is currently on display at the Museo Galileo in Florence.
  • He got something right again!
  • Galileo’s dad begrudgingly allowed him to leave medicine in favor of mathematics and died a few years later when Galileo was an amateur math professor—he had no idea his son was anything special, let alone “the Father of Modern Science.”
  • It is true that Vincenzo Galilei was not particularly enthusiastic when his son abandoned his medical studies, however Galileo was never an “amateur math professor” but a fully paid professional. On the “Father of Modern Science”, see above.

2014 equivalent: Elon Musk

I find the concept of Elon Musk being the 2014 equivalent of Galileo Galilei quite simply mindboggling!

Mr Urban your term paper does not meet the required standards. Your research is to put it mildly very sloppy and personal prejudice is not a substitute for scholarly endeavour, therefore I cannot award you anything but an F!


Filed under History of Astronomy, History of science, Myths of Science, Renaissance Science

Comets and Heliocentricity: A Rough Guide

In the standard mythologised history of astronomy of the Early Modern Period comets are only mentioned once. We get told, in classical hagiographical manner, how Tycho Brahe observed the great comet of 1577 and thus smashed the crystalline spheres of Aristotelian cosmology freeing the way for the modern astronomy. That’s it for comets, their bit part in the drama that is the unfolding of the astronomical revolution is over and done with, don’t call us we’ll call you. The problem with this mythological account is that it vastly over emphasises the role of both Tycho and the 1577 comet in changing the view of the heavens and vastly under rates the role played by comets and their observations in the evolution of the new astronomy in the Early Modern Period. I shall deal with the crystalline spheres and their dissolution in a separate post and for now will follow the trail of the comets as they weave their way through the fifteenth, sixteenth and seventeenth centuries changing our perceptions of the heavens and driving the evolution of the new astronomy. I have dealt with various aspects of this story in earlier posts but rather than simple linking I will outline the whole story here.

In antiquity comets were a phenomenon to be marvelled at and to be feared. Strange apparitions lighting up the skies unpredictably and unexplainably, bringing with them, in the view of the astrology priests of earlier cultures, doom and disaster. As with almost all things Aristotle had categorised comets, fitting them into his grand scheme of things. Aristotle’s cosmology was a cosmology of spheres. In the centre resided the spherical earth, on the outer reaches it was enclosed in the sphere of the fixed stars. Between theses two were the spheres of the planets centred on and spreading outwards from the earth, Moon, Mercury, Venus,  Sun, Mars, Jupiter Saturn. This onion of celestial spheres was split into two parts by the sphere of the moon. Everything above this, superlunar, was perfect, unchanging and eternal, everything below, sublunar, imperfect, constantly changing and subject to decay. For Aristotle comets were a sublunar phenomenon and were not part of astronomy, being dealt with in his Meteorology, his book on atmospheric phenomena, amongst other things.

However Aristotle’s was not the only theory of comets in ancient Greek philosophy, the Stoics, whose philosophy was far more important and influential than Aristotle’s in late antiquity had a very different theory. For the Stoics the cosmos was not divided into two by the sphere of the moon but was a single unity permeated throughout by pneuma (whatever that maybe!). For them comets were not an atmospheric phenomenon, as for Aristotle, but were astronomical objects of some sort or other.

In the High Middle Ages as higher learning began to flourish one more in Europe it was Aristotle’s scientific theories, made compatible with Christian theology by Albertus Magnus and his pupil Thomas Aquinas, that was taught in the newly founded universities and so comets were again treated as atmospheric phenomena up to the beginning of the fifteenth century.

The first person to view comets differently was the Florentine physician and mathematicus Paolo dal Pozzo Toscanelli (1397–1482), best known for his letter and map supplied to the Portuguese Crown confirming the viability of Columbus’ plan to sail westwards to reach the spice islands. In the 1430s Toscanelli observed comets as if they were astronomical object tracing their paths onto star-charts thereby initiating a new approach to cometary observation. Toscanelli didn’t publish his observations but he was part of a circle humanist astronomers and mathematicians in Northern Italy who communicated with each other over their work both in personal conversation and by letter. In the early 1440s Toscanelli was visited by a young Austrian mathematician called Georg Aunpekh (1423–1461), better known today by his humanist toponym, Peuerbach. We don’t know as a fact that Toscanelli taught his approach to comet observation to the young Peuerbach but we do know that Peuerbach taught the same approach to his most famous pupil, Johannes Müller aka Regiomontanus (1436–1476), at the University of Vienna in the 1450’s. Peuerbach and Regiomontanus observed several comets together, including Halley’s Comet in 1456. Regiomontanus wrote up their work in a book, which included his thoughts on how to calculate correctly the parallax of a comparatively fast moving object, such as a comet, in order to determine its distance from earth. The books of Peuerbach and Regiomontanus, Peuerbach’s cosmology, New Theory of the Planets, published by Regiomontanus in Nürnberg in 1473, and their jointly authored epitome of Ptolemaeus’ Almagest, first published in Venice in 1496, became the standard astronomy textbooks for the next generation of astronomers, including Copernicus. Regiomontanus’ work on the comets remained unpublished at the time of his death.

Whereas in the middle of the fifteenth century, as Peuerbach and Regiomontanus were active there were very few competent astronomers in Europe the situation had improved markedly by the 1530s when comets again played a central role in the history of the slowly developing new astronomy. The 1530s saw a series of spectacular comets that were observed with great interest by astronomers throughout Europe. These observations led to a series of important developments in the history of cometary observation. Johannes Schöner (1477–1547) the Nürnberger astrologer-astronomer published Regiomontanus’ book on comets including his thoughts on the mathematics of measuring parallax, which introduced the topic into the European astronomical discourse. Later in the century Tycho Brahe and John Dee would correspond on exactly this topic. A discussion developed between various leading astronomers, including Peter Apian (1495–1552) in Ingolstadt, Nicolaus Copernicus (1473–1543) in Frauenburg, Gemma Frisius (1508–1555) in Leuven and Jean Péna (1528 or 1530–1558 or 1568) in Paris, on the nature of comets. Frisius and Pena in Northern Europe as well as Gerolamo Cardano (1501–1576) and Girolamo Fracastoro (circa 1476–1553) in Italy propagated a theory that comets were superlunar bodies focusing sunlight like a lens to produce the tail. This theory developed in a period that saw a major revival in Stoic philosophy. Apian also published his observations of the comets including what would become known, incorrectly, as Apian’s Law that the tails of comets always point away from the sun. I say incorrectly because this fact had already been known to Chinese astronomers for several centuries.

These developments in the theory of comets meant that when the Great Comet of 1577 appeared over Europe Tycho Brahe (1546–1601) was by no means the only astronomer, who followed it’s course with interest and tried to measure its parallax in order to determine whether it was sub- or superlunar. Tycho was not doing anything revolutionary, as it is normally presented in the standard story of the evolution of modern astronomy, but was just taking part in in a debate on the nature of comets that had been rumbling on throughout the sixteenth century. The results of these mass observations were very mixed. Some observers failed to make a determination, some ‘proved’ that the comet was sublunar and some, including Tycho on Hven, Michael Maestlin (1550–1631), Kepler’s teacher, in Tübingen and Thaddaeus Hagecius (1525–1600) in Prague, all determined it to be superlunar. There were many accounts published throughout Europe on the comet the majority of which still favoured a traditional Aristotelian astrological viewpoint of which my favourite was by the painter Georg Busch of Nürnberg. Busch stated that comets were fumes that rose up from the earth into the atmosphere where they collected and ignited raining back down on the earth causing all sorts of evils and disasters including Frenchmen.

On a more serious note the parallax determinations of Tycho et al led to a gradual acceptance amongst astronomers that comets are indeed astronomical and not meteorological phenomena, whereby at the time Maestlin’s opinion probably carried more weight than Tycho’s. This conclusion was given more substance when it was accepted by Christoph Clavius (1538–1612), who although a promoter of Ptolemaic astronomy, was the most influential astronomer in Europe at the end of the sixteenth century.

By the beginning of the seventeenth century comets had advanced to being an important aspect of astronomical research; one of the central questions being the shape of the comets course through the heavens. In 1607 the English astronomer, Thomas Harriot (circa 1560–1621), and his friend and pupil, the MP, Sir William Lower (1570–1615), observed Halley’s Comet and determined that its course was curved. In 1609/10 Harriot and Lower became two of the first people to read and accept Kepler’s Astronomia Nova, and Lower suggested in a letter to Harriot that comets also follow elliptical orbits making him the first to recognise this fact, although his view did not become public at the time.

The comet of 1618 was the source of one of the most famous disputes in the history of science between Galileo Galilei (1564–1642) and the Jesuit astronomer Orazio Grassi (1583–1654). Grassi had observed the comet, measured its parallax and determined that it was superlunar. Galileo had, due to an infirmity, been unable to observe the comet but when urged by his sycophantic fan club to offer an opinion on the comet couldn’t resist. Strangely he attacked Grassi adopting an Aristotelian position and claiming that comets arose from the earth and were thus not superlunar. This bizarre dispute rumbled on, with Grassi remaining reasonable and polite in his contributions and Galileo becoming increasingly abusive, climaxing in Galileo’s famous Il Saggiatore. The 1618 comet also had a positive aspect in that Kepler (1571–1630) collected and collated all of the available historical observational reports on comets and published them in a book in 1619/20 in Augsburg. Unlike Lower, who thought that comets followed Keplerian ellipses, Kepler thought that the flight paths of comets were straight lines.

The 1660s again saw a series of comets and by now the discussion amongst astronomers was focused on the superlunar flight paths of these celestial objects with Kepler’s text central to their discussions. This played a significant role in the final acceptance of Keplerian elliptical heliocentric astronomy as the correct model for the cosmos, finally eliminating its Tychonic and semi-Tychonic competitors, although some Catholic astronomers formally continued paying lip service to a Tychonic model for religious reasons, whilst devoting their attentions to discussing a heliocentric cosmos hypothetically.

The 1680s was a fateful decade for comets and heliocentricity. John Flamsteed (1646–1719), who had been appointed as the first Astronomer Royal in Greenwich in 1675, observed two comets in 1680, one in November and the second in mid December. Flamsteed became convinced that they were one and the same comet, which had orbited the sun. He communicated his thoughts by letter to Isaac Newton (1642–1727) in Cambridge, the two hadn’t fallen out with each other yet, who initially rejected Flamsteed’s findings. However on consideration Newton came to the conclusion that Flamsteed was probably right and drawing also on the observations of Edmund Halley began to calculate possible orbits for the comet. He and Halley began to pay particular attention to observing comets, in particular the comet of 1682. By the time Newton published his Principia, his study of cometary orbits took up one third of the third volume, the volume that actually deals with the cosmos and the laws of motion and the law of gravity. By showing that not only the planets and their satellite systems obeyed the law of gravity but that also comets did so, Newton was able to demonstrate that his laws were truly universal.

After the publication of the Principia, which he not only edited and published but also paid for out of his own pocket, Halley devoted himself to an intense study of the historical observations of comets. He came to the conclusion that the comet he had observed in 1682, the one observed by Peuerbach and Regiomontanus in Vienna in 1456 and the one observed by Harriot and Lower in London in 1607 were in fact one and the same comet with an orbital period of approximately 76 years. Halley published the results of his investigations both in the Philosophical Transactions of the Royal Society and as a separate pamphlet under the title Synopsis of the Astronomy of Comets in 1705. Halley determined the orbit of the comet that history would come to name after him and announced that it would return in 1758. Although long lived Halley had no hope of witness this return and would never know if his was right or not. Somewhat later the French Newtonian astronomer and mathematician Alexis Clairaut (1713–1765) recalculated the return date, introducing factors not considered by Halley, to within a one-month error of the correct date. The comet was first observed on Newton’s birthday, 25 December 1758 and reached perihelion, its nearest approach to the sun, on 13 March 1759, Clairault had predicted 13 April. This was a spectacular empirical confirmation of Newton’s theory of universal gravity and with it of heliocentric astronomy. Comets had featured in the beginnings of the development of modern astronomy in the work of Toscanelli, Peuerbach and Regiomontanus and then in the final confirmation of that astronomy with the return of Halley’s Comet having weaved their way through they whole story over the preceding 350 years.




Filed under History of Astronomy, History of science, Newton, Renaissance Science

The history of “scientist”

Today is a red-letter day for readers of The Renaissance Mathematicus; I have succeeded in cajoling, seducing, bullying, bribing, inducing, tempting, luring, sweet-talking, coaxing, coercing, enticing, beguiling[1] Harvard University’s very own Dr Melinda Baldwin into writing a guest post on the history of the term scientist, in particular its very rocky path to acceptance by the scientific community. First coined by William Whewell at the third annual meeting of the British Association for the Advancement of Science in 1833 in response to Samuel Taylor Coleridge’s strongly expressed objection to men of science using the term philosopher to describe themselves, the term experienced a very turbulent existence before its final grudging acceptance almost one hundred years later. In her excellent post Melinda outlines that turbulent path to acceptance, read and enjoy.


J.T. Carrington, editor of the popular science magazine Science-Gossip, achieved a remarkable feat in December of 1894: he found a subject on which the Duke of Argyll (a combative anti-Darwinian) and Thomas Huxley (a.k.a. “Darwin’s bulldog”) held the same opinion.

Carrington had noticed the spread of a particular term related to scientific research. He himself felt the word was “not satisfactory,” and he wrote to eight prominent writers and men of science to ask if they considered it legitimate. Seven responded. Huxley and Argyll joined a five-to-two majority when they denounced the term. “I regard it with great dislike,” proclaimed Argyll. Huxley, exhibiting his usual gift for witty dismissals, said that the word in question “must be about as pleasing a word as ‘Electrocution.’”

The word? “Scientist.”

Duke of Argyll

Duke of Argyll

Thomas Huxley

Thomas Huxley

Today “scientist” is not only an accepted title—it is a coveted one. To be a “scientist” is to be someone with an acknowledged right to make knowledge claims about the natural world. However, as the 1894 debate suggests, the term has a fraught history among English-speaking scientific practitioners. In retrospect, Huxley and Argyll’s rejection of “scientist” might seem merely quaint, even petty. But the history of the word “scientist” is not just a linguistic curiosity. Debates over its acceptance or rejection were, in the end, not about the word itself: they were about what science was, and what place its practitioners held in their society.

William Whewell

William Whewell

The English academic William Whewell first put the word “scientist” into print in 1834 in a review of Mary Somerville’s On the Connexion of the Physical Sciences. Whewell’s review argued that science was becoming fragmented, that chemists and mathematicians and physicists had less and less to do with one another. “A curious illustration of this result,” he wrote, “may be observed in the want of any name by which we can designate the students of the knowledge of the material world collectively.” He then proposed “scientist,” an analogue to “artist,” as the term that could provide linguistic unity to those studying the various branches of the sciences.

Most nineteenth-century scientific researchers in Great Britain, however, preferred another term: “man of science.” The analogue for this term was not “artist,” but “man of letters”—a figure who attracted great intellectual respect in nineteenth-century Britain. “Man of science,” of course, also had the benefit of being gendered, clearly conveying that science was a respectable intellectual endeavor pursued only by the more serious and intelligent sex.

“Scientist” met with a friendlier reception across the Atlantic. By the 1870s, “scientist” had replaced “man of science” in the United States. Interestingly, the term was embraced partly in order to distinguish the American “scientist,” a figure devoted to “pure” research, from the “professional,” who used scientific knowledge to pursue commercial gains.

“Scientist” became so popular in America, in fact, that many British observers began to assume that it had originated there. When Alfred Russel Wallace responded to Carrington’s 1894 survey he described “scientist” as a “very useful American term.” For most British readers, however, the popularity of the word in America was, if anything, evidence that the term was illegitimate and barbarous.


Nature Masthead

Nature Masthead

Feelings against “scientist” in Britain endured well into the twentieth century. In 1924, “scientist” once again became the topic of discussion in a periodical, this time in the influential specialist weekly Nature. In November, the physicist Norman Campbell sent a Letter to the Editor of Nature asking him to reconsider the journal’s policy of avoiding “scientist.” He admitted that the word had once been problematic; it had been coined at a time “when scientists were in some trouble about their style” and “were accused, with some truth, of being slovenly.” Campbell argued, however, that such questions of “style” were no longer a concern—the scientist had now secured social respect. Furthermore, said Campbell, the alternatives were old-fashioned; indeed, “man of science” was outright offensive to the increasing number of women in science.

In response, Nature’s editor, Sir Richard Gregory, decided to follow in Carrington’s footsteps. He solicited opinions from linguists and scientific researchers about whether Nature should use “scientist.” The word received more support in 1924 than it had thirty years earlier. Many researchers wrote in to say that “scientist” was a normal and useful word that was now ensconced in the English lexicon, and that Nature should use it.

However, many researchers still rejected “scientist.” Sir D’Arcy Wentworth Thompson, a zoologist, argued that “scientist” was a tainted term used “by people who have no great respect either for science or the ‘scientist.’” The eminent naturalist E. Ray Lankester protested that any “Barney Bunkum” might be able to lay claim to such a vague title. “I think we must be content to be anatomists, zoologists, geologists, electricians, engineers, mathematicians, naturalists,” he argued. “‘Scientist’ has acquired—perhaps unjustly—the significance of a charlatan’s device.”

In the end, Gregory decided that Nature would not forbid authors from using “scientist,” but that the journal’s staff would continue to avoid the word. Gregory argued that “scientist” was “too comprehensive in its meaning … The fact is that, in these days of specialized scientific investigation, no one presumes to be ‘a cultivator of science in general.’” And Nature was far from alone in its stance: as Gregory observed, the Royal Society of London, the British Association for the Advancement of Science, the Royal Institution, and the Cambridge University Press all rejected “scientist” as of 1924. It was not until after the Second World War that Campbell would truly get his wish for “scientist” to become the accepted British term for a person who pursued scientific research.

Tracing the acceptance or rejection of “scientist” among researchers not only gives us a history of a word—it also provides insight into the self-image of scientific researchers in the English-speaking world in a time when the social and cultural status of “science” was undergoing tremendous changes. Interestingly, the history of “scientist” shows that the word’s adoption cannot be straightforwardly associated with the professionalization of the sciences. “Scientist” was used in America to separate scientific researchers from “professionals.” In Britain, many researchers viewed “scientist” as a term that threatened their social and intellectual identity, a term that would open science up to any “Barney Bunkum” rather than confirm it as a selective, expert endeavor. Perhaps those who denounced the word might have been reassured by a glimpse into the future of the “scientist”—or perhaps they would still think that “scientists” might be better off as zoologists, chemists, and physicists.

Further reading on the word “scientist”:

Melinda Baldwin, Making Nature: The History of a Scientific Journal (Chicago: University of Chicago Press, forthcoming 2015).

Paul Lucier, “The Professional and the Scientist in Nineteenth-Century America,” Isis 100 (2009): 699-732.

Sydney Ross, “Scientist: The Story of a Word,” Annals of Science 18 (1962): 65-85.

Laura J. Snyder, The Philosophical Breakfast Club: Four Remarkable Friends who Transformed Science and Changed the World (New York: Broadway Books, 2012).

[1] Actually I just asked her and she said, yes.


Filed under History of science

Planetary Tables and Heliocentricity: A Rough Guide

Since it emerged sometime in the middle of the first millennium BCE the principal function of mathematical astronomy was to provide the most accurate possible predictions of the future positions of the main celestial bodies. This information was contained in the form of tables calculated with the help of the mathematical models, which had been derived by the astronomers from the observed behaviour of those bodies, the planets. The earliest Babylonian models were algebraic but were soon replaced by the Greeks with geometrical models based on spheres and circles. To a large extent it did not matter if those models were depictions of reality, what mattered was the accuracy of the prediction that they produced; that is the reliability of the associated tables. The models of mathematical astronomy were judge on the quality of the data they produced and not on whether they were a true reproduction of what was going on in the heavens. This data was used principally for astrology but also for cartography and navigation. Mathematical astronomy was a handmaiden to other disciplines.

Before I outline the history of such tables, a brief comment on terminology. Data on the movement of celestial bodies is published under the titles planetary tables and ephemerides (singular ephemeris). I know of no formal distinction between the two names but as far as I can determine planetary tables is generally used for tables calculated for quantitatively larger intervals, ten days for example, and these are normally calculated directly from the mathematical models for the planetary movement. Ephemeris is generally used for tables calculated for smaller interval, daily positions for example, and are often not calculated directly from the mathematical models but are interpolated from the values given in the planetary tables. Maybe one of my super intelligent and incredibly well read readers knows better and will correct me in the comments.

The Babylonians produced individual planetary tables, in particular of Venus, but we find the first extensive set in the work of Ptolemaeus. He included tables calculated from his geometrical models in his Syntaxis Mathematiké (The Almagest), published around 150 CE, and to make life easier for those who wished to use them he extracted the tables and published them separately, in extended form with directions of their use, in what is known as his Handy Tables. This publication provided both a source and an archetype for all future planetary tables.

The important role played by planetary tables in mathematical astronomy is illustrated by the fact that the first astronomical works produced by Islamic astronomers in Arabic in the eighth-century CE were planetary tables known in Arabic as zījes (singular zīj). These initial zījes were based on Indian sources and earlier Sassanid Persian models. These were quickly followed by those based on Ptolemaeus’ Handy Tables. Later sets of tables included material drawn from Islamic Arabic sources. Over 200 zījes are known from the period between the eighth and the fifteenth centuries. Because planetary tables are dependent on the observers geographical position most of these are only recalculation of existing tables for new locations. New zījes continued to be produced in India well into the eighteenth-century.

With the coming of the European translators in the twelfth and thirteenth centuries and the first mathematical Renaissance the pattern repeated itself with zījes being amongst the first astronomical documents translated from Arabic into Latin. Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī was originally better known in Europe for his zīj than for The Compendious Book on Calculation by Completion and Balancing” (al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala), the book that introduced algebra into the West. The Toledan Tables were created in Toledo in the eleventh-century partially based on the work of Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Zarqālī, known in Latin as Arzachel. In the twelfth-century they were translated in Latin by Gerard of Cremona, the most prolific of the translators, and became the benchmark for European planetary tables.

In the thirteenth- century the Toledan Tables were superseded by the Alfonsine Tables, which were produced by the so-called Toledo School of Translators from Islamic sources under the sponsorship of Alfonso X of Castile. The Alfonsine Tables remained the primary source of planetary tables and ephemerides in Europe down to the Renaissance where they were used by Peuerbach, Regiomontanus and Copernicus. Having set up the world’s first scientific press Regiomontanus produced the first ever printed ephemerides, which were distinguished by the accuracies of their calculations and low level of printing errors. Regiomontanus’ ephemerides were very popular and enjoyed many editions, many of them pirated. Columbus took a pirate edition of them on his first voyage to America and used them to impress some natives by accurately predicting an eclipse of the moon.

By the fifteenth-century astronomers and other users of astronomical data were very much aware of the numerous inaccuracies in that data, many of them having crept in over the centuries through frequent translation and copying errors. Regiomontanus was aware that the problem could only be solved by collecting new basic observational data from which to calculate the tables. He started on such an observational programme in Nürnberg in 1470 but his early death in 1475 put an end to his endeavours.

When Copernicus published his De revolutionibus in 1543 many astronomers hoped that his mathematical models for the planetary orbits would lead to more accurate planetary tables and this pragmatic attitude to his work was the principle positive reception that it received. Copernicus’ fellow professor of mathematic in Wittenberg Erasmus Reinhold calculated the first set of planetary tables based on De revolutionibus. The Prutenic Tables, sponsored by Duke Albrecht of Brandenburg Prussia (Prutenic is Latin for Prussian), were printed and published in 1551. Ephemerides based on Copernicus were produced by Johannes Stadius, a student of Gemma Frisius, in 1554 and by John Feild (sic), with a forward by John Dee, in 1557. Unfortunately they didn’t live up to expectations. The problem was that Copernicus’ work and the tables were based on the same corrupted data as the Alfonsine Tables. In his unpublished manuscript on navigation Thomas Harriot complained about the inaccuracies in the Alfonsine Tables and then goes on to say that the Prutenic Tables are not any better. However he follows this complaint up with the information that Wilhelm IV of Hessen-Kassel and Tycho Brahe on Hven are gathering new observational data that should improve the situation.

As a young astronomer the Danish aristocrat, Tycho Brahe, was indignant that the times given in both the Alfonsine and the Prutenic tables for a specific astronomical event that he wished to observe were highly inaccurate. Like Regiomontanus, a hundred years earlier, he realised that the problem lay in the inaccurate and corrupted data on which both sets of tables were based. Like Regiomontanus he started an extensive programme of astronomical observations to solve the problem, initially at his purpose built observatory financed by the Danish Crown on the island of Hven and then later, through force of circumstances, under the auspices of Rudolph II, the Holy Roman German Emperor, in Prague. Tycho devoted almost thirty years to accruing a vast collection of astronomical data. Although he was using the same observational instruments available to Ptolemaeus fifteen hundred years earlier, he devoted an incredible amount of time and effort to improving those instruments and the methods of using them, meaning that his observations were more accurate by several factors than those of his predecessors. What was now needed was somebody to turn this data into planetary tables, enter Johannes Kepler. Kepler joined Tycho in Prague in 1600 and was specifically appointed to the task of producing planetary tables from Tycho’s data. Contrary to popular belief he was not employed by Tycho but directly by Rudolph.

Following Tycho’s death, a short time later, a major problem ensued. Kepler was official appointed Imperial Mathematicus, as Tycho’s successor, and still had his original commission to produce the planetary tables for the Emperor, however, legally, he no longer had the data; this was Tycho’s private property and on his death passed into the possession of his heirs. Kepler was in physical possession of the data, however, and hung on to it during the protracted, complicated and at times vitriolic negotiations with Tycho’s son in law, Frans Gansneb Genaamd Tengnagel van de Camp, over their future use. In the end the heirs granted Kepler permission to use the data with the proviso that any publications based on them must carry Tengnagel’s name as co-author. Kepler then proceeded to calculate the tables.

Put like this, it sounds like a fairly straightforward task, however it was difficult and tedious work that Kepler loathed intensely. It was not made any easier by the personal and political circumstances surrounding Kepler over the years he took to complete the task. Wars, famine, usurpation of the Emperor’s throne (don’t forget the Emperor was his employer) and family disasters all served to make his life more difficult.

Finally in 1626, twenty-six years after he started Kepler had finally reduced Tycho’s thirty years of observations into planetary tables for general use, now he only had to get them printed. Drumming up the financial resources for the task was the first hurdle that Kepler successfully cleared. He then purchased the necessary paper and settled in Linz to complete the task of turning his calculations into a book. As the printing was progressing all the Protestants in Linz were ordered to leave the city, Kepler, being Imperial Mathematicus, and his printer were granted an exemption to finish printing the tables but then Wallenstein laid siege to the city to supress a peasants uprising. In the ensuing chaos the printing shop and the partially finished tables went up in flames.

Leaving Linz Kepler now moved to Ulm where, starting from the beginning again, he was finally able to complete the printing of the Rudophine Tables, named after the Emperor who had originally commissioned them but dedicated to the current Emperor, Ferdinand II. Although technically not his property, because he had paid the costs of having them printed Kepler took the finished volumes to the book fair in Frankfurt to sell in September 1627.

Due to the accuracy of Tycho’s observational data and the diligence of Kepler’s mathematical calculations the new tables were of a level of accuracy never seen before in the history of astronomy and fairly quickly became the benchmark for all astronomical work. Perceived to have been calculated on the basis of Kepler’s own elliptical heliocentric astronomy they became the most important artefact in the general acceptance of heliocentricity in the seventeenth century. As already stated above systems of mathematical astronomy were judged on the data that they produced for use by astrologers, cartographers, navigators et al. Using the Rudolphine Tables Gassendi was able to predict and observe a transit of Mercury in 1631, as Jeremiah Horrocks succeeded in predicting and observing a transit of Venus for the first time in human history based on his own calculations of an ephemeris for Venus using Kepler’s tables, it served as a confirming instance of the superiority of both the tables and Kepler’s elliptical astronomy, which was the system that came to be accepted by most working astronomers in Europe around 1660. The principle battle in the war of the astronomical systems had been won by a rather boring set of mathematical tables, Johannes Kepler’s Tabulae Rudolphinae.

Rudolphine Tables Frontispiece

Rudolphine Tables Frontispiece




Filed under History of Astrology, History of Astronomy, History of Cartography, History of Navigation, History of science, Renaissance Science